C Challenge

38. Surveying A surveyor wants to mark off a triangular parcel with an area of 1 acre ( 1  acre  = 43   , 560   ft 2 ) . open 1 , acre , equals 43 comma . 560 , ft squared , close .  One side of the triangle extends 300 ft along a straight road. A second side extends at an angle of 65 ° 65 degrees  from one end of the first side. What is the length of the second side to the nearest foot?
39. Segments are drawn between the midpoints of consecutive sides of a regular pentagon to form another regular pentagon. Find, to the nearest hundredth, the ratio of the area of the smaller pentagon to the area of the larger pentagon.

Standardized Test Prep

SAT/ACT

GRIDDED RESPONSE

40. A regular polygon has a perimeter of 54 m and an apothem of 3 3 m . 3 square root of 3 m .  What is the area of the polygon to the nearest tenth of a square meter?
41. The legs of a right triangle have lengths of 8 in. and 15 in. What is the length of the hypotenuse in inches?
42. Δ P E N ≅ Δ L I V . cap delta p e n , approximately equal to . cap delta l i v .  If m ∠ P = 36 m angle , p equals 36  and m ∠ N = 82   , m angle . n equals 82 comma  what is m ∠ I ? m angle i question mark
43. The perimeter of a parallelogram is 23.6 ft. If its length and width are doubled, what is the perimeter of the parallelogram in feet?
44. The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 8 and 10. What is the length of the shorter leg of the triangle?

Mixed Review

See Lesson 10-4.

45. Two regular octagons are shown.

    1. What is the scale factor of the smaller octagon to the larger octagon?
    2. The area of the larger octagon is 391 . 1   in . 2 . 391 . 1 in , . squared , .  What is the area of the smaller octagon to the nearest tenth of a square inch?

       

See Lesson 8-5.

For Exercises 46–49, use vectors a ⇀ modified a with right harpoon up above  and C ⇀ c with right harpoon up above  below.

46. What is the sum of a ⇀ modified a with right harpoon up above  and C ⇀ c with right harpoon up above  as an ordered pair?
47. Describe a vector d ⇀ modified d with right harpoon up above  such that a ⇀ + d ⇀ = C ⇀ . modified a with right harpoon up above , plus , modified d with right harpoon up above , equals , c with right harpoon up above , .
48. Describe a vector e ⇀ modified e with right harpoon up above  such that C ⇀ + e ⇀ = a ⇀ . c with right harpoon up above , plus , modified e with right harpoon up above , equals , modified a with right harpoon up above , .
49. Which two vectors have C ⇀ c with right harpoon up above  as their sum?

    〈 − 2 , − 2 〉 〈 2 , − 4 〉 〈 4 , − 2 〉 left pointing angle bracket , negative 2 comma . negative 2 , right pointing angle bracket . left pointing angle bracket , 2 comma . negative 4 , right pointing angle bracket . left pointing angle bracket , 4 comma . negative 2 , right pointing angle bracket

Get Ready! To prepare for Lesson 10-6, do Exercises 50–52.

See Lesson 1-8.

Find the diameter or radius of each circle.

50. r = 7   cm , d = □ r equals 7 cm comma . d equals white square
51. d = 5   in. , r = □ d equals 5 in. comma . r equals white square
52. r = 1   . 6   m , d = □ r equals 1 . 6 m comma d equals white square

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